Transparent conducting oxides (TCOs) play an essential role in modern optoelectronic devices through their combination of electrical conductivity and optical transparency. We review recent progress in our understanding of multi-component TCOs formed from solid solutions of ZnO, In(2)O(3), Ga(2)O(3) and Al(2)O(3), with a particular emphasis on the contributions of materials modelling, primarily based on density functional theory. In particular, we highlight three major results from our work: (i) the fundamental principles governing the crystal structures of multi-component oxide structures including (In(2)O(3))(ZnO)(n) and (In(2)O(3))(m)(Ga(2)O(3))(l)(ZnO)(n); (ii) the relationship between elemental composition and optical and electrical behaviour, including valence band alignments; (iii) the high performance of amorphous oxide semiconductors. On the basis of these advances, the challenge of the rational design of novel electroceramic materials is discussed.
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